Constant dollars is an abstract concept which allows us to legitimately compare results obtained in different years.  One of the insidious properties of inflation is that the value of the dollar changes from year to year.  That makes it incorrect to directly compare dollar amounts earned or stated in different years.  The correct way to compare amounts earned in different years is to convert them to a common base time, or a common base year as follows:

            S_m = S_n / (1+ r)^(n-m)       (m<n)

where   r  = the rate of inflation
                        S_m= equivalent amount in year m
                        S_n= equivalent amount in year n
                        m = any particular year < n (such as 1999)
                        n  = any particular year > m (such as 2007)

It follows that the converse holds as:

            S_n = S_m ·(1+ r)^(n-m)        (m<n)                                                                                             

When we convert to constant dollars, it is appropriate to place a subscript on the dollar sign to differentiate the amounts from each other.  For example:

$₀            (which is read as dollars at time j=0)    
$₅₀          (which is read as dollars at time j=50)  
$₁₉₉₉       (which is read as dollars in year 1999, or 1999 dollars)
$₂₀₀₇       (which is read as dollars in year 2007, or 2007 dollars) 

©2008, Simon Revere Mouer III
all rights reserved